3x(x+1)=270

Solution for 3x(x+1)=270 equation:

3x(x+1)=270

We move all terms to the left:

3x(x+1)-(270)=0

We multiply parentheses

3x^2+3x-270=0

a = 3; b = 3; c = -270;
Δ = b2-4ac
Δ = 32-4·3·(-270)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-57}{2*3}=\frac{-60}{6}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+57}{2*3}=\frac{54}{6}
=9
$